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In this talk we investigate some classes of real valued functions with specific view of describing their sets of continuity and differentiability. The approach requires the use of Baire Category Theorem which has subtle and unexpected applications in many areas of Analysis. Dr. Marius Ghergu is an expert in the field of Analysis and is just as passionate about it now as he was when he was a student. This talk should be accessible for second year undergraduates upwards but all are welcome to attend as it should be very insightful. The zoom link for this talk can be found on our social media platforms closer to the time. Facebook: https://www.facebook.com/UcdMathsoc Instagram: https://www.instagram.com/ucdmathsoc/ Discord: https://discord.gg/SEzHDGG